The average response time for http requests at a web server is 2.5 seconds. The system idle time was measured to be 12 seconds during a one minute observation interval. Use an M/M/1 model for the system to determine the following (a) system utilization (b) average service time per transaction (c) probability that the number of jobs in the system exceeds 10
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The average response time for http requests at a web server is 2.5 seconds. The system idle time was measured to be 12 seconds during a one minute observation interval. Use an M/M/1 model for the system to determine the following
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(a) system utilization
-
(b) average service time per transaction
-
(c) probability that the number of jobs in the system exceeds 10
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- During nearly four decades of business operations, Memphis-based FedEx has earned a reputation for reliable, on-time delivery of packages to homes and offices around the country. Founder Fred Smith originally focused on overnight deliveries, choosing Memphis as the company’s headquarters because the airport rarely closes due to bad weather. With FedEx’s planes departing and arriving on schedule nearly all the time, its express shipments usually remained on schedule, then and now. To reassure customers that delivery will take place when and where promised, the firm offers a money-back guarantee on time-sensitive express shipments, among other services. FedEx has steadily expanded its portfolio of services since the 1970s. Its original overnight express delivery is currently available to U.S. customers in various forms, including “first-overnight” delivery, next-morning delivery, next-afternoon delivery, and budget-pleasing two- or three-day delivery. The company’s services also include cost-effective ground delivery for parcels and extra-speedy same-day delivery for urgent deliveries within 1,800 cities. Over the years, FedEx has widened its delivery network to more than 220 countries. It has purchased more cargo jets and acquired specialized shipping firms, including Tiger International, Roberts Express, RPS, and TNT Express, to support global growth. For international business customers needing products, parts, or raw materials shipped across countries or continents, the company now offers time-saving services such as commercial freight forwarding and cross-border logistical support. To add the convenience of local drop-off and pickup points for U.S. consumers and small businesses, FedEx acquired the Kinko’s office services company in 2004 and later rebranded it as FedEx Office. This acquisition also added printing and copying to the menu of services offered. Then the company arranged for large U.S. retailers such as Walgreens, Albertsons, Kroger, and Safeway to accept packages for shipment and receive package delivery for customer pickup in thousands of store locations. This means people who want to send a package can head to a nearby retailer and ship where they shop, rather than making a separate trip to the FedEx location. It’s also a safe alternative for packages to be picked up by people who don’t want FedEx shipments left by the front door. Another service FedEx offers to small and mid-sized businesses, including retailers, is FedEx Fulfillment. The purpose is to expedite order fulfillment by having each business store its products in a FedEx warehouse. Then, when the business’s customers place orders, FedEx puts the products into boxes bearing the business’s own logo and ships directly to those customers. The business doesn’t need a separate warehouse or staff for fulfillment, and packages are on their way to customers more quickly because the products were in FedEx’s warehouse, ready to be packed and shipped. This service puts FedEx into direct competition with Amazon.com, which offers a similar service to merchants that sell through the online Amazon Marketplace. But it also gives businesses that don’t sell via Amazon a fast and professional fulfillment alternative. FedEx is careful to let customers know, through media and social-media announcements, when it anticipates that extreme weather or other conditions will cause delays or force it to halt pickups and deliveries. For the duration of Hurricane Irma, for example, FedEx said it would suspend deliveries in Florida. Some Florida customers who had ordered generators to be delivered via FedEx were unhappy, because they worried about being without power during and after the storm. But one FedEx employee loaded several generator orders into his car and took them to customers himself. When a customer posted a grateful compliment to FedEx on Facebook, the message generated thousands of likes, shares, and positive comments. The company also received positive comments for its donations of cash and transportation services to areas devastated by Hurricanes Irma, Harvey, and Maria. According to the American Customer Satisfaction Index (ACSI), FedEx often tops the list of U.S. shipping companies as ranked by customers surveyed. Every day, the company delivers 13 million packages—and during the busy year-end holiday season, it delivers many more. By meeting customers’ expectations for on-time deliveries, FedEx has increased annual revenues beyond $60 billion and positioned itself for continued growth in the future. How does FedEx’s money-back guarantee address customers’ concerns about heterogeneity?At the beginning of each week, a machine is in one of four conditions: 1 = excellent; 2 = good; 3 = average; 4 = bad. The weekly revenue earned by a machine in state 1, 2, 3, or 4 is 100, 90, 50, or 10, respectively. After observing the condition of the machine at the beginning of the week, the company has the option, for a cost of 200, of instantaneously replacing the machine with an excellent machine. The quality of the machine deteriorates over time, as shown in the file P10 41.xlsx. Four maintenance policies are under consideration: Policy 1: Never replace a machine. Policy 2: Immediately replace a bad machine. Policy 3: Immediately replace a bad or average machine. Policy 4: Immediately replace a bad, average, or good machine. Simulate each of these policies for 50 weeks (using at least 250 iterations each) to determine the policy that maximizes expected weekly profit. Assume that the machine at the beginning of week 1 is excellent.A crew of mechanics at the Department of Transportation garage make minor repairs to snowplows during the winter. The snowplows break down at an average rate of 5 vehicles per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 8 vehicles per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day. What are the chances that 3 vehicles are in the service system? Group of answer choices 9% 38% 63% 19%
- Repair calls are handled by one repairman at a photocopy shop. Repair time, including travel time, is exponentially distributed, with a mean of 2.5 hours per call. Requests for copier repairs come in at a mean rate of 2.1 per eight-hour day (assume Poisson). a. Determine the average number of customers awaiting repairs. (Round your answer to 2 decimal places.) Number of customers b. Determine system utilization. (Round your answer to the nearest whole percent. Omit the "%" sign in your response.) System utilization % c. Determine the amount of time during an eight-hour day that the repairman is not out on a call. (Use your rounded answer from Part b. Round your answer to 2 decimal places.) Amount of time hours d. Determine the probability of two or more customers in the system. (Do not round intermediate calculations. Round your answer to…The new-accounts officer at the Bank enrolls all new customers in checking accounts. During the three-week period in August encompassing the beginning of the new school year at UTT, the bank opens many new accounts for students. The bank estimates that the arrival rate during this period will be Poisson distributed with an average of five (5) customers per hour. The service time is exponentially distributed with an average of 15 minutes per customer to set up a new account. The bank wants to determine the operating characteristics for this system to determine if the current person is sufficient to handle the increased traffic. What is the probability of no customers in the system? What is the average number of customers waiting in the bank? What is the average time the customer spends in the bank? What is the average number of customers waiting in the line? What is the average time that a customer spends in the line? Is the number of tellers sufficient to handle the increase…A mechanic at the Department of Maintenance makes minor repairs to faulty golf electric carts. The carts break down at an average rate of 4 carts per day and breakdowns are distributed according to the Poisson distribution. The mechanic can service an average of 6 carts per day with a repair time distribution that approximates a negative exponential distribution. Assume an 8 hour day. a- What is the utilization rate for the mechanic? b- What is the average time in hours that a cart is out of service?
- An airline is planning to open a satellite ticket desk in a new shopping plaza, staffed byone ticket agent. It is estimated that requests for tickets and information will average15 per hour and requests will have a Poisson distribution. Service time is assumed to be exponentially distributed. Previous experience with similar satellite operations suggeststhat mean service time should average about three minutes per request. Determine each ofthe following:a. System utilizationb. Percentage of time the server (agent) will be idlec. The expected number of customers waiting to be servedd. The average time customers will spend in the systeme. The probability of zero customers in the system and the probability of four customersin the system.Failsafe Textiles employs three highly skilled maintenance workers who are responsible for repairing the numerous industrial robots used in its manufacturing process. A worker can fix one robot every 8 hours on average, with an exponential distribution. An average of one robot fails every 3 hours, according to a Poisson distribution. Each down robot costs the company $100.00 per hour in lost production. A new maintenance worker costs the company $80.00 per hour in salary, benefits, and equipment. Should the manager hire any new personnel? If so, how many people? What would yourecommend to the manager, based on your analysis?You are the manager of a local bank where three tellers provide services to customers. On average, each teller takes 3 minutes to serve a customer. Customers arrive, on average, at a rate of 50 per hour. Having recently received complaints from some customers that they waited a long time before being served, your boss asks you to evaluate the service system.Specifically, you must provide answers to the following questions:a. What is the average utilization of the three-teller service system?b. What is the probability that no customers are being served by a teller or are waiting in line?c. What is the average number of customers waiting in line?d. On average, how long does a customer wait in line before being served?e. On average, how many customers would be at a teller’s station and in line?
- Gilman Heating and Air Conditioning Gilman Heating and Air Conditioning Inc. provides a broad range of services to commercial and residential customers, including installation and repair of several different brands of heating and air-conditioning systems, Gilman has a fleet of 28 trucks, each operated by one or more service technicians, depending on the size of a job. A recurrent problem for Gilman has been coordinating the service teams during the day to determine the status of a job and the need for parts not kept in the service vehicle, as well as to identify which team to send on emergency calls. Gilman's service area is spread over an urban/rural area of approximately 50 square miles. The company has developed cost and price sheets so that the service technicians accurately and consistently price the service work they perform.Repair calls are handled by one repairman at a photocopy shop. Repair time, including travel time, is exponentially distributed, with a mean oftwo hours per call. Requests for copier repairs come in at a mean rate of three per eight-hour day(assume Poisson). Determine the following: ( l) The average number of customers awaiting repairs (2) System utilization (3) The amount of time during an eight-hour day that the repairman is not out on a call (4) The probability of two or more customers in the system4) Repair calls are handled by one repairman at a photocopy shop. Repair time, including travel time, is exponentially distributed, with a mean of two hours per call. Requests for copier repairs come in at a mean rate of three per eight- hour day (assume Poisson). Determine:1. The average number of customers awaiting repairs.2. System utilization.3. The amount of time during an eight-hour day that the repairman is not out on a call. 4. The probability of two or more customers in the system.